Conventionally, a shunt-peaking technique is widely used to effectively increase the circuit bandwidth. FIG. 1A is a schematic circuit diagram of a conventional amplifying circuit. FIG. 1B is a plot illustrating the relationships between the gain value and the frequency of the amplifying circuit of FIG. 1A.
As shown in FIG. 1A, the amplifying circuit 100 comprises a transistor T, a capacitor C, a resistor R and an inductor L. The resistor R and the inductor L are connected with each other in series and collaboratively considered as an inductive load 110.
The gate terminal of the transistor T is an input terminal of the amplifying circuit 100 for receiving an input signal vi. The drain terminal of the transistor T is an output terminal of the amplifying circuit 100 for outputting an output signal vo. The source terminal of the transistor T is connected to a ground terminal. The resistor R and the inductor L are serially connected between a voltage source Vdd and the output terminal of the amplifying circuit 100. The capacitor C is connected between the output terminal of the amplifying circuit 100 and the ground terminal.
Please refer to the spectrum diagram of FIG. 1B. If the inductor L is not included in the amplifying circuit 100 (i.e. L=0), the amplifying circuit 100 has a bandwidth x. Whereas, if the inductor L is included in the amplifying circuit 100, the bandwidth of the amplifying circuit 100 gradually increases with the increasing inductance value.
In case that the inductor L of the amplifying circuit 100 has the optimal inductance value Lopt, the bandwidth of the amplifying circuit 100 is approximately equal to 1.7x. In other words, the bandwidth of the amplifying circuit 100 having the inductor L with the optimal inductance value Lopt is about 1.7 times the bandwidth of the amplifying circuit 100 having no inductor. For example, the optimal inductance value Lopt is 0.4R2C for a maximally flat frequency response.
Moreover, in case that the inductance value of the inductor L is higher than the optimal inductance value Lopt, the gain value at the corner frequency increases. In other words, the inductor L of the amplifying circuit 100 can further increase the bandwidth of the amplifying circuit 100 if gain peaking of around 20% can be tolerated.
Generally, for designing IC circuitry, the inductor can be designed on a two-dimensional plane. However, the area budget of this type of IC circuitry is often constrained, it is difficult to design the inductor having the optimized performance within reasonable area. For increasing the circuit bandwidth, an active inductor was disclosed. Since the active inductor has the characteristics of the conventional inductor, the active inductor may be applied to the amplifying circuit.
FIG. 2A is a schematic circuit diagram of a conventional active inductor. FIG. 2B is a schematic circuit diagram illustrating a small signal model of the conventional active inductor of FIG. 2A. FIG. 2C is a plot illustrating the relationships between the impedance and the frequency of the conventional active inductor of FIG. 2A. The active inductor 210 may be connected to the output terminal of the amplifying circuit 100 as shown in FIG. 1A in order to replace the inductive load 110 of the amplifying circuit 100.
As shown in FIG. 2A, the active inductor 210 comprises a transistor M and a resistor R. The resistor R is connected between the gate terminal of the transistor M and the voltage source Vdd. The drain terminal of the transistor M is connected to the voltage source Vdd.
Please refer to FIG. 2B. In the small signal model of the active inductor 210, a parasitic capacitor Cgs is connected between the gate terminal and the source terminal of the transistor M. According to a gate-source voltage signal vgs, a current flows through the drain terminal and the source terminal. The magnitude of the small signal current is equal to gm×vgs, wherein gm is a transconductance value of the transistor M.
Please refer to FIG. 2C, which illustrates the relationships between the impedance and the frequency of the conventional active inductor 210. In case that the frequency is lower than ωz, the magnitude of the small-signal impedance (|z(jω)|) is 1/gm. In case that the frequency is higher than oz, the magnitude of the impedance (|z(jω)|) rises and reaches its maximum of R. If R>1/gm, the active inductor 210 has lower impedance in the lower frequency band and higher impedance in the higher frequency band. Consequently, the active inductor 210 may be considered as the inductive load.
FIG. 3 is a schematic circuit diagram of another conventional active inductor. The active inductor 310 may be connected to the output terminal of the amplifying circuit 100 as shown in FIG. 1A in order to replace the inductive load 110 of the amplifying circuit 100.
As shown in FIG. 3, the active inductor 310 comprises a transistor M, a capacitor L and a resistor R. The drain terminal of the transistor M is connected to a first voltage source Vdd. The resistor R is connected between the gate terminal of the transistor M and a second voltage source Vbh. The capacitor C is connected between the second voltage source Vbh and a ground terminal. Generally, the relationships between the impedance and the frequency of the active inductor 310 are similar to the relationships between the impedance and the frequency of the active inductor 210, and are not redundantly described herein. Moreover, the active inductor 310 may be considered as the inductive load.